Simplify the following expression: $a = \dfrac{3q^2 + 42q + 144}{q + 8} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $3$ , so we can rewrite the expression: $ a =\dfrac{3(q^2 + 14q + 48)}{q + 8} $ Then we factor the remaining polynomial: $q^2 + {14}q + {48} $ ${8} + {6} = {14}$ ${8} \times {6} = {48}$ $ (q + {8}) (q + {6}) $ This gives us a factored expression: $\dfrac{3(q + {8}) (q + {6})}{q + 8}$ We can divide the numerator and denominator by $(q - 8)$ on condition that $q \neq -8$ Therefore $a = 3(q + 6); q \neq -8$